A379615
Numerators of the partial sums of the reciprocals of the sum of bi-unitary divisors function (A188999).
Original entry on oeis.org
1, 4, 19, 107, 39, 61, 259, 89, 93, 857, 887, 181, 1303, 331, 1345, 4091, 4175, 21127, 4301, 21757, 87973, 88813, 90073, 90577, 1192621, 1201981, 1211809, 1221637, 1234741, 1240201, 626243, 89909, 45247, 15169, 30533, 153601, 2941819, 2956639, 20807623, 20876783
Offset: 1
Fractions begin with 1, 4/3, 19/12, 107/60, 39/20, 61/30, 259/120, 89/40, 93/40, 857/360, 887/360, 181/72, ...
- Amiram Eldar, Table of n, a(n) for n = 1..1000
- V. Sitaramaiah and M. V. Subbarao, Asymptotic formulae for sums of reciprocals of some multiplicative functions, J. Indian Math. Soc., Vol. 57 (1991), pp. 153-167.
- László Tóth, Alternating Sums Concerning Multiplicative Arithmetic Functions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1. See section 4.13, p. 34.
-
f[p_, e_] := (p^(e+1) - 1)/(p - 1) - If[OddQ[e], 0, p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ f @@@ FactorInteger[n]; Numerator[Accumulate[Table[1/bsigma[n], {n, 1, 50}]]]
-
bsigma(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^(f[i, 2]+1) - 1)/(f[i, 1] - 1) - if(!(f[i, 2] % 2), f[i, 1]^(f[i, 2]/2)));}
list(nmax) = {my(s = 0); for(k = 1, nmax, s += 1 / bsigma(k); print1(numerator(s), ", "))};
A379616
Denominators of the partial sums of the reciprocals of the sum of bi-unitary divisors function (A188999).
Original entry on oeis.org
1, 3, 12, 60, 20, 30, 120, 40, 40, 360, 360, 72, 504, 126, 504, 1512, 1512, 7560, 1512, 7560, 30240, 30240, 30240, 30240, 393120, 393120, 393120, 393120, 393120, 393120, 196560, 28080, 14040, 4680, 9360, 46800, 889200, 889200, 6224400, 6224400, 889200, 1778400
Offset: 1
- Amiram Eldar, Table of n, a(n) for n = 1..1000
- V. Sitaramaiah and M. V. Subbarao, Asymptotic formulae for sums of reciprocals of some multiplicative functions, J. Indian Math. Soc., Vol. 57 (1991), pp. 153-167.
- László Tóth, Alternating Sums Concerning Multiplicative Arithmetic Functions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1. See section 4.13, p. 34.
-
f[p_, e_] := (p^(e+1) - 1)/(p - 1) - If[OddQ[e], 0, p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ f @@@ FactorInteger[n]; Denominator[Accumulate[Table[1/bsigma[n], {n, 1, 50}]]]
-
bsigma(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^(f[i, 2]+1) - 1)/(f[i, 1] - 1) - if(!(f[i, 2] % 2), f[i, 1]^(f[i, 2]/2)));}
list(nmax) = {my(s = 0); for(k = 1, nmax, s += 1 / bsigma(k); print1(denominator(s), ", "))};
A379617
Numerators of the partial alternating sums of the reciprocals of the sum of bi-unitary divisors function (A188999).
Original entry on oeis.org
1, 2, 11, 43, 53, 4, 37, 103, 23, 65, 71, 337, 2539, 1217, 2539, 7337, 7757, 1501, 7883, 7631, 31469, 30629, 31889, 6277, 84625, 82753, 423593, 82753, 426869, 421409, 216847, 213727, 108911, 11899, 24253, 119081, 2317139, 760853, 773203, 6889667, 7037867, 13946059
Offset: 1
Fractions begin with 1, 2/3, 11/12, 43/60, 53/60, 4/5, 37/40, 103/120, 23/24, 65/72, 71/72, 337/360, ...
-
f[p_, e_] := (p^(e+1) - 1)/(p - 1) - If[OddQ[e], 0, p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ f @@@ FactorInteger[n]; Numerator[Accumulate[Table[(-1)^(n+1)/bsigma[n], {n, 1, 50}]]]
-
bsigma(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^(f[i, 2]+1) - 1)/(f[i, 1] - 1) - if(!(f[i, 2] % 2), f[i, 1]^(f[i, 2]/2)));}
list(nmax) = {my(s = 0); for(k = 1, nmax, s += (-1)^(k+1) / bsigma(k); print1(numerator(s), ", "))};
A379618
Denominators of the partial alternating sums of the reciprocals of the sum of bi-unitary divisors function (A188999).
Original entry on oeis.org
1, 3, 12, 60, 60, 5, 40, 120, 24, 72, 72, 360, 2520, 1260, 2520, 7560, 7560, 1512, 7560, 7560, 30240, 30240, 30240, 6048, 78624, 78624, 393120, 78624, 393120, 393120, 196560, 196560, 98280, 10920, 21840, 109200, 2074800, 691600, 691600, 6224400, 6224400, 12448800
Offset: 1
-
f[p_, e_] := (p^(e+1) - 1)/(p - 1) - If[OddQ[e], 0, p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ f @@@ FactorInteger[n]; Denominator[Accumulate[Table[(-1)^(n+1)/bsigma[n], {n, 1, 50}]]]
-
bsigma(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^(f[i, 2]+1) - 1)/(f[i, 1] - 1) - if(!(f[i, 2] % 2), f[i, 1]^(f[i, 2]/2)));}
list(nmax) = {my(s = 0); for(k = 1, nmax, s += (-1)^(k+1) / bsigma(k); print1(denominator(s), ", "))};
Showing 1-4 of 4 results.